For a cylindrical conductor with a hollow center, let the radius from the axis to the inner circle be a and the radius from the axis to the outer circle be b , as shown below. Note that the region from the axis to a is hollow while the region between a and b is a conductor. We assume that the current I in the cylindrical conductor is uniformly spread into the cross-section between a and b Calculate the magnitude of magnetic field at a distance from the axis where: • r b Plot the magnitude of the magnetic field with respect to the distance r from the axis.

Question 1: The magnetic flux of a uniform magnetic field of magnitude B througn a flat area A whose area vector is at angle with the magnetic field is given by ... (select the best choice) OBXA OBA sin OBA OAX B OBA cos Part (a) › analyzes the directions of the forces between two parallel wires carrying currents in the same direction. Perform a similar analysis for the forces between two parallel wires carrying currents in opposite directions. Those forces are... (select the best choice) Orepulsive to the left Part (b) Oto the right Oup Odown O attractive two ways of determining the direction of the magnetic field produced at some point by a moving charge or a current. Which hand or hands are avolved in both ways? (select the best choice) OBoth hands, but mainly the right ORight hand OBoth hands equally OLeft hand ONone of the other choices

A rectangular wire loop of height h, width w, and net electrical resistance R lies in the x-y plane. As shown in the figure below, the entire region x < 0 of space is occupied by a constant, uniform magnetic field which points in the –z direction (into the page). In order to determine the magnitude of this field, a student pulls the wire loop out of the magnetic field region at a constant velocity v in the +x-direction, and measures the current I induced in the loop during this process. I = 17 μAR = 35 ohmsh = 3 cm w = 8 cmv = 2 cm/sec a) What is the direction of the current induced in the wire loop? b)What is the magnitude B of the magnetic field?

Problem 2 Show that in a current-free volume of space, a static magnetic field can never have a local maximum by considering V(B· B) · da, where S is the surface of a small volume V containing a point P in space.